Nano-positioners may be used to move objects of different sizes with a nanometer-level or a better precision. The nano-positioners are important as they set limits on an ability to measure, understand, manipulate, and manufacture physical systems. Compliant apparatus, i.e. flexures, are ideal for the ultra-precision motion guidance and possess advantages (no wear between joint members and free of backlash etc.) over traditional mechanical linkages in precision motion applications. However, there is a limitation for flexure-based nano-positioners, that is, high-bandwidth flexure-guided nano-positioners have a relatively small travel range, while large-displacement flexure-based nano-positioners have low natural frequencies, e.g. the resonant frequency of a millimeter-ranged nano-positioner is less than 100 Hz.